Thursday, March 31, 2016

An Earthlike Planet

The press is full of
the news that a new Earthlike planet, Kepler 452b, has been discovered by the
revived Kepler planet-hunting
spacecraft.The discovery of a planet
“much like Earth” garners more attention because the planet orbits in the
so-called “Goldilocks zone” around its star, the range of distances within
which water can exist as a liquid on its surface rather than only as ice or hot
vapor.

Kepler 452b is 60%
larger in diameter than Earth and is presumed to have Earthlike composition,
although it is important to note that there is as yet no way of measuring its
mass.Nonetheless, the phrase “Earthlike
world” has the press reeling, including suggestions that worlds like this are
the places radio astronomers should look to find radio signals from intelligent
aliens.

OK, let’s play this
game and see what Earthlike composition would imply.A diameter of 1.6 times Earth’s means a
surface area of 1.6x1.6, or 2.56 times Earth’s, and a volume of 1.6x2.56, or
4.1 times Earth’s.Assuming Earthlike
material, this planet would have a core/mantle/crust structure very similar to
Earth’s, but the internal pressures would of course be significantly higher,
and the core and mantle material must be compressed to higher density than
Earth’s average of 5.5 grams per cubic centimeter, probably close to 7.5 for
the whole planet.Now, that would
generate a planet with 5.6 times Earth’s mass.This mass and diameter would correspond to a surface gravity that is
5.6/2.56 times Earth, 2.18 times as large, or 21.4 meters/second2.

“Similar composition”
means similar abundances of radioactive elements, which decay inside the planet
and eventually lose their heat by radiating heat from the planetary surface
into space.This planet, generating 5.6
times as much heat as Earth, which it radiates into space through a surface
with area 2.56 times Earth’s, so the heat flux (Watts per square meter per
second) is about 2.2 times Earth’s.At
steady state, with heat loss rate equal to heat production rate, this requires
that the temperature gradient in the crust (the rate at which temperature
increases with depth) must be 2.2 times as large as on Earth.

Mountains can build up
only to a finite height because the temperature gradient under them leads to
softening and melting of the continental rock deep under them.On Earth the Himalayas rise about 13
kilometers above the abyssal plains of the oceans.Mars has half the radius of Earth, so its
heat flow and temperature gradient should be about half that of Earth, meaning
that softening of the rock should occur about twice as deep, and Martian
mountains should build to about twice the height as on Earth.In fact, the highest peak on Mars, Olympus
Mons, rises about 26 km above the plains.Of course, to calculate this precisely we need to account for the
slightly lower density of Mars and its slightly lower surface temperature, but
we still get a similar answer.

Now let’s apply that to
Kepler 452b.The topography, Earth’s
standard scaled down by a factor of 2.2, would have the highest mountain regions
about 6 kilometers above the abyssal plains.Now let’s think about the oceans on this world.On Earth, there is enough water to make a
layer about 4 km deep covering the entire planet.Kepler 452b, if it has the same composition
as Earth, would contain 5.6 times as much water spread out over a surface area
that is 2.56 times as large.Thus it
would contain enough water to make a layer 2.56 times as deep as Earth’s 4 km,
or about 10.2 km deep.Since the highest
land would rise about 6 km from the abyssal plains, this means that the tops of
the highest mountains would lie roughly 4 km below mean sea level.Thus
Kepler 452b, if truly Earthlike in composition, would be a true water world.

Now consider the
conditions on the sea floor.An ocean
10.2 km deep in a gravity field of 2.2 Earth gravities would exert tremendous
pressure at the ocean floor: the weight of the ocean exerts an average pressure
of 2240 atmospheres, which is essentially the highest pressure at which pure
liquid water can exist, irrespective of temperature.At approximately this pressure, water freezes
to make dense (sinking) ice III rather than familiar (floating) ice I.Such an ocean could start to freeze from the
bottom up.

We’re also told the planet
has had liquid water for 6 billion years or more, without mentioning how the
luminosity of its parent star (and the surface temperature of the planet) have
changed over time.

Of course, with data on
the mass of the planet we could see whether it really is a “terrestrial” planet
or a sort of warmed-up ice ball: if the latter is the case, then the planet
could be much less dense and the ocean much deeper.

So this is “Earth
2.0”?

If you are interested
in the wonderful game of designing planets that accord with the laws of
physics, astronomy, and chemistry, you can find a number of examples in my 1998
book Worlds without End, which
explores the possibilities for many types of planets allowed by nature, but not
present in our Solar System.

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John S. Lewis

John S. Lewis is a professor emeritus of planetary science at the University of Arizona’s Lunar and Planetary Laboratory and is Chief Scientist at Deep Space Industries. His interests in the chemistry and formation of the solar system and the economic development of space have made him a leading proponent of turning potentially hazardous near-Earth objects into lucrative space resources. Prior to joining the University of Arizona, Lewis taught space sciences and cosmochemistry at the Massachusetts Institute of Technology. He received his education at Princeton University, Dartmouth College and the University of California, San Diego, where he studied under Nobel Laureate Harold Urey. An expert on the composition and chemistry of asteroids and comets, Lewis has written such popular science books as "Mining the Sky", "Rain of Iron and Ice", and "Worlds without End".